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PreprintCC BY 4.0arXiv

Vertex operator algebra realizations of untwisted Haagerup--Izumi centers

  • David E. Evans
  • Andrew Riesen
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Abstract

For every odd integer N≥3, we construct an untwisted Haagerup--Izumi fusion category ℋN on the negative spherical branch and a simple, self-contragredient, regular, C2-cofinite vertex operator algebra EN of central charge −16N, together with an equivalence of modular fusion categories: Rep(EN)≃ Z(ℋN). The VOA EN is rational, has exactly N2+3 irreducible modules, and is lower bounded and integer graded, with least conformal degree −(N−1)/2. The proof begins with a CFT-type cyclic Virasoro extension of central charge −5N, whose regularity we establish. Two categorical condensations recover ℋN, and a finite extension by shifted lattice modules removes the auxiliary pointed factor. We identify the complete ribbon modular data of Z(ℋN) with MD−(ℤ/N;ℤ/(N2+4),b↦ b2/(N2+4)) in the notation of Gannon--Schopieray--Yadav, for every odd N.

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Cite

BibTeXRIS
BibTeX
@misc{evans2026vertex,
  title = {{Vertex operator algebra realizations of untwisted Haagerup--Izumi centers}},
  author = {David E. Evans and Andrew Riesen},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.32928},
  eprint = {2610.32928},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.32928},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Vertex operator algebra realizations of untwisted Haagerup--Izumi centers
AU  - David E. Evans
AU  - Andrew Riesen
PY  - 2026
DA  - 2026/10/23
PB  - arXiv
DO  - 10.48550/arxiv.2610.32928
UR  - https://arxiv.org/abs/2610.32928
AB  - For every odd integer N≥3, we construct an untwisted Haagerup--Izumi fusion category ℋ_N on the negative spherical branch and a simple, self-contragredient, regular, C_2-cofinite vertex operator algebra E_N of central charge −16N, together with an equivalence of modular fusion categories: Rep(E_N)≃ Z(ℋ_N). The VOA E_N is rational, has exactly N^2+3 irreducible modules, and is lower bounded and integer graded, with least conformal degree −(N−1)/2. The proof begins with a CFT-type cyclic Virasoro extension of central charge −5N, whose regularity we establish. Two categorical condensations recover ℋ_N, and a finite extension by shifted lattice modules removes the auxiliary pointed factor. We identify the complete ribbon modular data of Z(ℋ_N) with MD_−(ℤ/N;ℤ/(N^2+4),b↦ b^2/(N^2+4)) in the notation of Gannon--Schopieray--Yadav, for every odd N.
ER  -